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(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L11a320 at Knotilus!

Link Presentations

[edit Notes on L11a320's Link Presentations]

Planar diagram presentation X10,1,11,2 X2,11,3,12 X12,3,13,4 X20,5,21,6 X14,8,15,7 X16,14,17,13 X8,16,1,15 X22,17,9,18 X18,21,19,22 X6,9,7,10 X4,19,5,20
Gauss code {1, -2, 3, -11, 4, -10, 5, -7}, {10, -1, 2, -3, 6, -5, 7, -6, 8, -9, 11, -4, 9, -8}
A Braid Representative
A Morse Link Presentation L11a320 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in u, v, w, ...) -\frac{(t(2) t(1)-t(1)+1) (t(1) t(2)-t(2)+1) (2 t(2) t(1)-t(1)-t(2)+2)}{t(1)^{3/2} t(2)^{3/2}} (db)
Jones polynomial q^{3/2}-3 \sqrt{q}+\frac{6}{\sqrt{q}}-\frac{11}{q^{3/2}}+\frac{14}{q^{5/2}}-\frac{18}{q^{7/2}}+\frac{17}{q^{9/2}}-\frac{15}{q^{11/2}}+\frac{12}{q^{13/2}}-\frac{7}{q^{15/2}}+\frac{3}{q^{17/2}}-\frac{1}{q^{19/2}} (db)
Signature -3 (db)
HOMFLY-PT polynomial a^7 z^5+3 a^7 z^3+3 a^7 z-a^5 z^7-4 a^5 z^5-6 a^5 z^3-3 a^5 z+a^5 z^{-1} -a^3 z^7-4 a^3 z^5-6 a^3 z^3-4 a^3 z-a^3 z^{-1} +a z^5+3 a z^3+2 a z (db)
Kauffman polynomial -z^5 a^{11}+2 z^3 a^{11}-z a^{11}-3 z^6 a^{10}+5 z^4 a^{10}-2 z^2 a^{10}-5 z^7 a^9+7 z^5 a^9-2 z^3 a^9-6 z^8 a^8+10 z^6 a^8-10 z^4 a^8+7 z^2 a^8-4 z^9 a^7+2 z^7 a^7+z^5 a^7+z^3 a^7-2 z a^7-z^{10} a^6-10 z^8 a^6+27 z^6 a^6-30 z^4 a^6+13 z^2 a^6-7 z^9 a^5+11 z^7 a^5-5 z^5 a^5+z^3 a^5-z a^5-a^5 z^{-1} -z^{10} a^4-8 z^8 a^4+24 z^6 a^4-22 z^4 a^4+6 z^2 a^4+a^4-3 z^9 a^3+z^7 a^3+11 z^5 a^3-12 z^3 a^3+5 z a^3-a^3 z^{-1} -4 z^8 a^2+9 z^6 a^2-4 z^4 a^2-3 z^7 a+9 z^5 a-8 z^3 a+3 z a-z^6+3 z^4-2 z^2 (db)

Khovanov Homology

The coefficients of the monomials t^rq^j are shown, along with their alternating sums \chi (fixed j, alternation over r).   
\ r
j \
4           1-1
2          2 2
0         41 -3
-2        72  5
-4       85   -3
-6      106    4
-8     78     1
-10    810      -2
-12   58       3
-14  27        -5
-16 15         4
-18 2          -2
-201           1
Integral Khovanov Homology

(db, data source)

\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z} i=-4 i=-2
r=-8 {\mathbb Z}
r=-7 {\mathbb Z}^{2}\oplus{\mathbb Z}_2 {\mathbb Z}
r=-6 {\mathbb Z}^{5}\oplus{\mathbb Z}_2^{2} {\mathbb Z}^{2}
r=-5 {\mathbb Z}^{7}\oplus{\mathbb Z}_2^{5} {\mathbb Z}^{5}
r=-4 {\mathbb Z}^{8}\oplus{\mathbb Z}_2^{7} {\mathbb Z}^{8}
r=-3 {\mathbb Z}^{10}\oplus{\mathbb Z}_2^{7} {\mathbb Z}^{7}
r=-2 {\mathbb Z}^{8}\oplus{\mathbb Z}_2^{10} {\mathbb Z}^{10}
r=-1 {\mathbb Z}^{6}\oplus{\mathbb Z}_2^{8} {\mathbb Z}^{8}
r=0 {\mathbb Z}^{5}\oplus{\mathbb Z}_2^{6} {\mathbb Z}^{7}
r=1 {\mathbb Z}^{2}\oplus{\mathbb Z}_2^{4} {\mathbb Z}^{4}
r=2 {\mathbb Z}\oplus{\mathbb Z}_2^{2} {\mathbb Z}^{2}
r=3 {\mathbb Z}_2 {\mathbb Z}

Computer Talk

Much of the above data can be recomputed by Mathematica using the package KnotTheory`. See A Sample KnotTheory` Session.

Modifying This Page

Read me first: Modifying Knot Pages

See/edit the Link Page master template (intermediate).

See/edit the Link_Splice_Base (expert).

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